Abstract
The translation of a problem situation into a mathematical model constitutes a key – but not at all obvious – step in the modelling process. We focus on two elements that can hinder that translation process by relating it to the phenomenon of students’ overreliance on the linear model and their (lack of) representational fluency. We investigated: (1) How accurate are students in connecting descriptions of realistic situations to “almost” linear models, and (2) Does accuracy and model confusion depend on the representational mode in which a model is given? Results highlight that students confuse linear and non-linear models, and that the representational mode has a strong impact on this confusion: Correct reasoning about a situation with one mathematical model can be facilitated in a particular representation, while the same representation is misleading for situations with another model.
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Notes
- 1.
In this chapter we use the term linear to determine models that can be described by a formula of the form “y = ax”. Models that can be described by a formula of the form “y = ax + b” with b ≠ 0 are labelled as affine models. The term “almost” linear is used as a collective term for inverse linear and affine models, that is models that share some but not all characteristics with the linear model.
- 2.
In the rest of this chapter, we will use the term “representation” to denote “external representation”.
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Van Dooren, W., De Bock, D., Verschaffel, L. (2013). How Students Connect Descriptions of Real-World Situations to Mathematical Models in Different Representational Modes. In: Stillman, G., Kaiser, G., Blum, W., Brown, J. (eds) Teaching Mathematical Modelling: Connecting to Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6540-5_32
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